Can anybody explain it to me?
What exactly is your question? The only answer to the question as you have phrased it is "because that's the way the metre is defined"! If you used some other unit for length, you would get another number. In texts on relativity it is common to assume 1 "light-second" as the unit of length so that the speed of light is 1.
If your question is really "why is the speed of light the same in all frames of reference" I doubt that any one can give you a simple answer.
"why is the speed of light the same in all frames of reference"
nope, not that.
OK, why does the speed of light appear to be the speed it is when measured?
What initial condition caused it to be the speed we observe it at, and not 10m/s for instance?
Because some ignorant sadistic idiots from the Bureau of Sèvres wanted the the change the definition of the meter for the third time in 200 years (1983),but just 22 years after the previous.They wanted in terms of the speed of light in vacuo (considered by the GR as a "fundamental invariant" in the universe) and the second,for which they had previously come up with a strong definiton in terms of the Cesium atom's energy levels.But expreriment at that time left "c" with a numerical value of about 299792456,11645657957656975765795766967000876087775085580...m/s,anyway,not a fixed number.So they wanted it to fix it,to make it exact and beyond change & decimals,so they chose 299792458 m/s and they said that this is EXACT BY CONVENTION.Having done so,the new definition of meter was immediate.Logically,the meter is defined in terms of 2 concepts:"speed of light in vacuo" and the "second".
So that was your intial question...If i tell u this is still an open problem in modern physics and cosmology,would u believe me??If i told that scientists believe that immediately after the BB its value was larger (maybe much larger) and that "c" is decreasing with time (cosmological time)???
Each theory came up with it's own version of cosmology.SM came with the BB.GR came with the BB.Yet the theory which apparently incorporates best GR and QFT/SM,the string/superstring/M theory comes up with a staggering version on cosmology,saying there was no "big bang" and that the universe had 11 dimensions and be filled with interacting 10 dim.superstrings floating in the 11-th dimention.
For the SM version of BB,see Steven Weinberg's book"The first 3 minutes".
For why was there a BB (the GR version) see the book by Hawking and Ellis:"The large scale structure od space-time".
Ignorant sadistic idiiots??????????????????????????
Units of measure aside, the speed of light is determined by the permeability and permittivity constants, which are in turn measures of the electric and magnetic properties of space.
Ah, so my question is why are the permeability and permittivity constants the values they are.
Back in the days when the meter was a pair of lines on a bar kept in a box in Paris, the speed of light was a number that was measured. When it became clear that our distance standard (the physical bar) was limiting the precision with which we could measure the speed of light, we changed the standards to something more precise and repeatable than the use of this physical artifact. The first change was to specify a certain number of wavelengths of a particular transition frequency, but this defintion was found wanting. So eventually the meter was defined in terms of the speed of light, because that allowed for the most precise and repeatable definition of the meter.
The reason the numerical values that exist were chosen were for compatibility with the "old" meter. The intent was that the "new" meter and the "old" meter would be the same for all practical purposes, just that the new meter would be more precise than the old meter ever could be. So historical compatibility with a pair of marks on a bar was the reason that the speed of light has the numerical value it does today. The length between the marks on the bar originally had it's own motivation at the time it was created, but I don't recall all the details, I believe it was supposed to be some fraction of the Earth's circumference.
I think the question is more about fundamental relationships rather than our arbitrary choice of units, but the point is completely valid that the actual value is an artificial construct.
First we got the permittivity constant from Coulomb's Law, then the permeability constant from the Biot-Savart law, and Maxwell combined these to predict the known measured value of the speed of light as the speed of a traveling electromagnetic wave. This suggested the EM nature of light.
I believe the meter was modified so that the permeability constant has the precise factor of 4 pi.
These two constants - permeability and permittivity - are determined experimentally and they were long considered to be fundamental. I assume that String Theory can or will [if the theory is correct] predict these constants by using yet more fundamental values, but I don't know if must be true.
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